The problem is allowing there to be old vs. new contracts, not the control itself. There wouldn't be a black market for contracts if the price of rent for a unit was permanent, public information, and tied to the property. Even if it's sold, renovated, whatever - if the rent can literally never go up, sooner or later it's going to make financial sense to sell it. It might not be today, it might not be next week, but someday, the goal is to force as much of the property ownership in to the hands of people who want to be property owners and live in the properties.

It would have no effect on people who own and live in their home (except on the value of the property, if it causes a mass flood of properties on the market... which I doubt. The properties are still valuable just by virtue of being a place to live, they don't need the rent generating component to be valuable).